During the drilling of subterranean boreholes, high levels of rotational oscillation of the drillstring may occur; the drillstring going through cycles of rotational acceleration and deceleration. In some situations this can lead to “stick-slip” occurring, in which the bit or portions of the drillstring are at rest or even turn backwards.
These oscillations can be influenced by the choice of drill bit and the force and rotation speed applied to the drill bit. The generation of these oscillations has been attributed to a rotational force acting on the bit that reduces with increased rotation speed.
However, “stick-slip” oscillations have also been observed in drillstrings when rotating off-bottom, for example while running into hole. This is generally a feature of wells in which a substantial portion of the borehole is either horizontal or near-horizontal (also known as high-angle wells). It has been empirically determined that the oscillations become more severe as the hole lengthens and as the torque required to rotate the drillstring increases.
While observationally it may be seen that “friction” of some kind is a contributory agent in generating rotational oscillations, it has not previously been determined what properties of the frictional interaction are necessary for the generation of rotational oscillations, or how they may be interpreted, measured or estimated.
Nonetheless, it is often necessary to estimate and measure frictional parameters for use in the planning, simulation and monitoring of wells, especially those that deviate substantially from the vertical.
In modelling the torque and drag behaviour of drillstrings, it is conventional to use a Coulomb friction model for the tangential sliding contact between a drillstring and a borehole, i.e. the sliding contact at the sidewall of the borehole, not at the bit face. Such a model uses two friction coefficients (i.e. the model is based on the constant of proportionality between the frictional force and the normal side force): a dynamic friction coefficient for when the drillstring is moving relative to the borehole, and a static friction coefficient for when the drillstring is at rest. The dynamic friction coefficient is constant for changes in the relative velocity between the drillstring and the borehole, while the static friction coefficient is normally higher than the dynamic friction coefficient since the force (or torque) required to set a drillstring into motion is generally higher than that required to keep it in motion. According to this model, the friction coefficient changes instantaneously between the shift from static to the dynamic regime.
In Coulomb friction models for torque and drag, different friction coefficients may be used for tangential motion in different directions, for instance in SPE paper 19958 (M. S. Quigley et al., A Full-Scale Wellbore Friction Simulator, presented at IADC/SPE Drilling Conference, Houston, Tex., 27 Feb. to 2 Mar., 1990), significantly different dynamic Coulomb friction coefficients were experimentally measured for axial and rotational motion. In this paper, the variations with velocity direction of dynamic (not static) coefficients were measured.
During the drilling of boreholes with rotation induced at least in part by the rotation of the top of the drillstring, the tangential sliding contact velocity has components both along the axis of the borehole and normal to the axis (in the direction of rotation), however the component in the direction of rotation is normally greatly in excess of the component along the axis of the borehole—and thus, the detail of how the friction coefficient may vary with direction does not play a significant role in the determination of the drillstring dynamics. If the drillstring is not being rotated from the surface, but instead the drillbit is turned by a positive displacement motor close to the bit, or if the drillstring rotation is slow and the axial velocity is large (for instance, during slow reaming in or out of hole), then axial friction may be dominant or significant.
In the planning of wells, the torque necessary to turn the drillstring can be estimated for different values of the friction coefficient, and parameters such as the drillstring elements and the trajectory of the borehole can be adjusted so that for a range of reasonable values of the friction coefficient, the torque necessary to turn the drillstring at surface and drill ahead are within an acceptable range (e.g. below the maximum limit of the drill rig and also below the maximum torque allowable on the tubulars, which form the drillstring). Commonly, different values of friction coefficient are used for portions of the well that are lined with steel casing and the open hole (rock section) portions. It may also be taken into consideration that the friction coefficient in some parts of the well reduces over time due to polishing. For wells drilled in an area where there are existing wells of a similar type, likely values of the friction coefficient may be obtained by comparing observed torques in those wells with those predicted by different friction coefficients, and eliminating those values which are contradicted by observation.
A similar exercise is normally conducted for estimation of drag when the drillstring motion is axial (for instance pulling out of hole or running into hole, or to assess the forces on the drillstring when drilling without axial rotation from surface). As for torque, this modelling exercise can be conducted with a range of friction coefficients, and the drag values obtained with friction coefficients within the normal range can be used to assess whether the drilling operation can be satisfactorily conducted with the equipment available.
During the drilling of wells it is usual to monitor the torque as drilling proceeds, compare it to that expected with different values of the friction coefficient, and to use this to make updated predictions as to the torque required at latter stages of drilling the well. If lubricants are being used to reduce the friction coefficient, then the monitoring of torque and the comparison with the expected torque from different friction coefficients allows the effects of the lubricant to be assessed and the quantity of lubricant in the drilling fluid to be adjusted.